"We are not considering replacing Matt Lauer," Wallace said in a statement. "As we've said before, Matt is the best in the business. We want him in the 'Today' show anchor chair for many years to come."

The statement followed a Deadline Hollywood report that top NBC executives recently reached out to Cooper about replacing Lauer, but that Lauer objected and complained to Cooper.

Last April, Lauer signed a long-term contract to remain on "Today." (New York Magazine reports he negotiated a $25 million annual fee after threatening to jump ship to ABC.)

But that hasn't stopped speculation that Lauer is on his way out.

Cooper is in high demand as a theoretical replacement these days. Earlier this month, the New York Post reported that Cooper was in consideration to replace longtime "Jeopardy" host Alex Trebek when he retires. (Interestingly, Lauer was also mentioned as a possible replacement for Trebek.)

However, a person close to Cooper told TheWrap that he was not approached about hosting the game show.